Entropy solutions to noncoercive nonlinear elliptic equations with measure data
Date
2019-08-05
Authors
Huang, Shuibo
Su, Tong
Du, Xinsheng
Zhang, Xinqiu
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
Let Ω ⊆ ℝN be a bounded domain. In this article, we investigate the existence of entropy solutions to the nonlinear elliptic problem
-div (|∇u|(p-2) ∇u + c(x)uγ / (1 + |u|)θ(p-1) + b(x)|∇u|λ / (1 + |u|θ(p-1) = μ, x ∈ Ω,
u(x) = 0, x ∈ ∂Ω,
where μ is a diffuse measure with bounded variation on Ω, 0 ≤ θ < 1 is a positive constants, 1 < p < N, 0 < γ ≤ p - 1, 0 < λ ≤ p - 1, c(x) and b(x) belong to appropriate Lorentz spaces.
Description
Keywords
Entropy solution, Noncoercive, Nonlinear elliptic equations, Measure data
Citation
Huang, S., Su, T., Du, X., & Zhang, X. (2019). Entropy solutions to noncoercive nonlinear elliptic equations with measure data. <i>Electronic Journal of Differential Equations, 2019</i>(97), pp. 1-22.
Rights
Attribution 4.0 International